Problem Set Seven Solutions

Two automotive producers, Saab and Volvo, have fastened prices of $1 billion and fixed marginal prices of $10,000 per automotive. If Saab produces 50,000 vehicles per 12 months and Volvo produces 200,000, calculate the common fastened price and common whole price for every firm. On the idea of those prices, which firm’s market share ought to develop in relative phrases?

Reply: Common whole price is common fastened price plus marginal price: ATC = FC/Q + MC. Volvo’s common fastened price $1 billion/200,000 = 5,000 is far lower than Saab’s common fastened price $1 billion/50,000 = 20,000 because of producing extra vehicles.

Volvo’s common manufacturing price $15,000 is decrease than Saab’s of $30,000 by the distinction in common fastened prices. Volvo’s market share ought to develop relative to Saab’s. 6. What’s the socially fascinating value for a pure monopoly to cost? Why will a pure monopoly that makes an attempt to cost the socially optimum value invariably undergo an financial loss?

Reply: The socially fascinating value to cost is the one at which the marginal profit to shoppers equals the marginal price of manufacturing.

Nevertheless, pure monopolies often have very massive fastened prices and comparatively low marginal prices.

The excessive fastened prices imply that common price is bigger than marginal price, in order that charging a value equal to marginal price implies financial losses.

eight. Suppose that Aggieland Cinema is an area monopoly whose demand curve for normal grownup tickets on Saturday evening is P = 12 – 2Q, the place P is the worth of a ticket in dollars and Q is the variety of tickets offered in a whole lot.  The demand for scholar tickets on Sunday afternoon is P = eight – 3Q, and for normal grownup tickets on Sunday afternoon, P = 10 – 4Q. On each Saturday evening and Sunday afternoon, the marginal price of a further patron, scholar or not, is $2.

What’s the marginal income curve in every of the three markets?

Reply: The marginal income curves are MR = 12 – 4Q grownup Saturday evening, MR = eight – 6Q scholar Sunday afternoon, and MR = 10 – 8Q grownup Sunday afternoon.

b. What value ought to the cinema cost in every of the three markets to maximise earnings?

Reply: The cinema ought to choose amount to set marginal income equal to marginal price in every market after which set value for that amount based mostly on the demand curve for every market: 12 – 4Q = 2 yields Q = 250, so P = 12 – 2Q = 12 – 5 = $7 for normal adults on Saturday evening. – 6Q = 2 yields Q = 100, so P = eight – 3Q = eight – three = $5 for college kids on Sunday afternoon.

10 – 8Q = 2 yields Q = 100, so P = 10 – 4Q = 10 – four = $6 for normal adults on Sunday afternoon.

9. Suppose you’re a monopolist out there for a selected online game. Your demand curve is given by P = 80 – Q/2, and your marginal price curve is MC = Q.

Your fastened prices equal $400.

• a. Graph the demand and marginal price curve.
• b. Derive and graph (above) the marginal income curve.

Reply: MR = 80 – Q graphed above. c. Calculate and point out on the graph the equilibrium value and amount.

Reply: Choose amount to set marginal income equal to marginal price: 80 – Q = Q so Q = 40. Set value for that amount based mostly on the demand curve P = 80 – Q/2 = 80 – 40/2 = 80 – 20 = 60. d. What’s your revenue?

Reply: Whole income is value instances amount TR = PQ = (60)(40) = 2400. Whole price is fastened price plus common marginal price instances amount TC = 400 + (40)(40)/2 = 400 + 800 = 1200. Revenue = whole income – whole price = 2400 – 1200 = 1200. e.

What’s the degree of shopper surplus?

Reply: Shopper surplus is (half of)(80 – 60)(40) = 400. 10. Beth is a second-grader who sells lemonade on a avenue nook in your neighborhood. Every cup of lemonade prices Beth 20 cents to provide; she has no fastened prices. The reservation costs for the 10 individuals who stroll by Beth’s lemonade stand every hour are listed within the desk under. Beth is aware of the distribution of reservation costs (that’s, she is aware of one individual is keen to pay $1. 00, one other $zero. 90, and so forth), however doesn’t know any particular particular person’s reservation value.

a. Calculate the marginal income of promoting a further cup of lemonade. Begin by determining the worth Beth would cost if she produced just one cup of lemonade, and calculate the full income; then discover the worth she would cost if she offered two cups of lemonade; and so forth. ) Particular person Reservation value Amount in cups Whole income Marginal income A B C D E F G H I J $1. 00 $zero. 90 $zero. 80 $zero. 70 $zero. 60 $zero. 50 $zero. 40 $zero. 30 $zero. 20 $zero. 10 1 2 three four 5 6 7 eight 9 10 $1. 00 $1. 80 $2. 40 $2. 80 $three. 00 $three. 00 $2. 80 $2. 40 $1. 80 $1. 00 $1. 00 $zero. 80 $zero. 60 $zero. 40 $zero. 20 $zero -$zero. 20 -$zero. 40 -$zero. 60 -$zero. 80 b.

What’s Beth’s profit-maximizing value and amount?

Reply: MR = MC at a value of $zero. 60 and a amount of 5 cups. c. At that value, what are Beth’s financial revenue and whole shopper surplus?

Reply: Revenue = (P – MC) Q = (zero. 60 – zero. 20) 5 = $2. Shopper surplus is reservation value minus precise value for every cup offered: ($1. 00 – $zero. 60) + ($zero. 90 – $zero. 60) + ($zero. 80 – $zero. 60) + ($zero. 70 $zero. 60) = $1. d.

What value ought to Beth cost if she needs to maximise whole financial surplus? What amount would she promote? How a lot would whole financial surplus be?

Reply: She ought to set P = MC = $zero. 20. 9 (or eight) cups of lemonade can be offered.

Whole financial surplus is reservation value minus marginal price for every cup offered: ($1. 00 – $zero. 20) + ($zero. 90 – $zero. 20) + ($zero. 80 – $zero. 20) + ($zero. 70 – $zero. 20) + ($zero. 60 – $zero. 20) + ($zero. 50 – $zero. 20) + ($zero. 40 $zero. 20) + ($zero. 30 – $zero. 20) = $three. 60. e. Now suppose Beth can inform the reservation value of every individual. What value would she cost every individual if she needed to maximise revenue? Evaluate her revenue to the full surplus calculated partially d.

Reply: She would cost individuals A via I (however not J) their respective reservation costs. Doing so would earn a revenue of $three. 60, which is similar as the full financial surplus partially d.